Bucket falls in Class 21, housewares, and depending on what exactly you sell it can also fall in Class 7 or Class 10 or Class 25. Everything below is read from the USPTO's own list of accepted descriptions, not from an opinion about where it belongs.
Searching the USPTO Trademark ID Manual for bucket returns 40 accepted descriptions, and most of them sit in Class 21. The manual is the list of identifications the office has already approved, so wording taken from it is pre-approved and settles the class at the same time.
The class follows from the identification you write, so "what class am I in" is really "what exactly do you sell". How the class system works covers the rest.
Kitchenware, dishes, glassware, or household and cleaning utensils.
22 accepted descriptions in the manual mention bucket. For example:
Machines, power tools, motors, or engines (other than for land vehicles).
6 accepted descriptions in the manual mention bucket. For example:
Medical, surgical, dental, or veterinary instruments and health apparatus.
3 accepted descriptions in the manual mention bucket. For example:
Clothes, shoes, or hats.
2 accepted descriptions in the manual mention bucket. For example:
Bucket appears in 4 classes because what you make, what it is made of and the service of selling it are separate classes. Pick the descriptions above that match what you actually do.
Making bucket is Class 21; a shop or online store that sells it is retail store services (Class 35), and a business that does both files in both.
Household and kitchen utensils. Against Class 11 the test is electricity: non-electric kettles are here, electric kettles are there. Candle holders are here too, though the candles themselves are Class 4.
The class decides what a registration covers; it does not decide whether the name is available. Relatedness is judged on the identifications, so a conflict can sit in a class you never looked at: the same name in a different industry.
Check whether your name is clear for bucket Searches the live USPTO register, including sound-alike and meaning-alike names. First search $2, then $5.Bucket sits in Class 21, housewares. That is where the USPTO's own ID Manual puts it: 22 accepted descriptions mentioning bucket fall in Class 21. Depending on exactly what you sell it can also fall in Class 7 or Class 10 or Class 25.
You file in every class you actually use the mark in, and the USPTO charges its fee per class. Selling a product and also running an online store for it is two classes, not one. Filing in classes you do not use is worse than filing in too few: an application has to be supported by real use or a genuine intent to use.
No. The class decides what a registration covers. Availability turns on whether someone already holds a similar mark for related goods, and relatedness is judged on what the identifications say rather than on the class number, so marks in different classes can still conflict.
Not what you sell? Search the class finder for your own wording, or browse all 45 classes.